Imaging display technology has been subject to huge growth and technological advances. The ability of displays to provided higher and higher resolution images has resulted in a related increase in the size of the image data necessary to represent the displayed images. Moreover, electronic video displays are being implemented in increasingly smaller sizes. Personal phones and other devices provide users with high-quality view screens. Many of such devices provide access to various networks, such as the Internet, which allow for downloading of video content. Examples of important factors in such applications include processing power (in terms of larger processor size, increased power consumption and/or longer processing times) and bandwidth for video downloads. To compensate for bandwidth limitations, many applications related to the transmission of video content implement relatively complex video compression/coding techniques. Unfortunately, increasing the compression/coding complexity can lead to increases in the processing power necessary to code (i.e., encode or decode).
Many coding techniques use spatial and/or temporal compression techniques (downsampling) involving a transform that helps to decrease the amount of data used to represent the video image. One such transform is the 8×8 discrete cosine transform (DCT). Another type of transform is a wavelet transform. The output of the transform can be quantized to facilitate transmission and further encoding of the data. For example, entropy encoding can be used to further reduce the data size.
Certain types of video coding techniques use temporal redundancies in the video images to reduce the size of the encoded video. For example, various MPEG (and related) standards use predicted-frames (P-frames) or inter-frames to exploit similarities between images. For many applications much (or even all) of the image may remain the same for successive images. Some standards use previously transmitted image data to reproduce other images, thereby allowing a particular frame to be coded with only the differences between the current frame and a previous frame. More complex algorithms allow for compensation for motion of objects within successive frames. In particular, the difference between temporal frames can be determined using motion vectors to track similarities between frames where the similarities may have shifted within the video image. Such motion vectors indicate a possible correlation between pixels or portions of two different images. Generally, the motion vectors are the result of movement of objects within successive images; however, motion vectors can represent similarities between different images other than those resulting from movement of objects. The motion vector represents the difference, if any, in the positions of the pixels/portions of the different images. Such motion vector data will be embedded in the P-frame for use by the decoder. A specific type of motion compensation uses bidirectional-frames (B-frames). Such frames allow for the motion vectors from both the previous and future frames.
Hybrid video coding techniques as well as motion-compensated subband coding schemes can be used to generate data representing image sequences and used for coding and communication applications. To achieve high compression efficiency, some hybrid video encoders operate in a closed-loop fashion such that the total distortion across the reconstructed pictures equals the total distortion in the corresponding intra picture and encoded displaced frame differences. In case of transmission errors, decoded reference frames differ from the optimized reference frames at the encoder and error propagation is observed. On the other hand, transform coding schemes operate in an open-loop fashion. Such open-loop schemes include high-rate transform coding schemes in which the analysis transform produces independent transform coefficients. With uniform quantization, these schemes are optimal when utilizing an orthogonal transform. Further, energy conservation holds for orthogonal transforms such that the total quantization distortion in the coefficient domain equals that in the image domain. In case of transmission errors, the error energy in the image domain equals that in the coefficient domain. Hence, the error energy is preserved in the image domain and is not amplified by the decoder, as is the case, e.g., for predictive decoders.
During the last decade, there have been attempts to incorporate motion compensation into temporal subband coding schemes by approaching problems arising from multi-connected pixels. For example, some methods choose a reversible lifting implementation for the temporal filter and incorporate motion compensation into the lifting steps. In particular, the motion-compensated lifted Haar wavelet maintains orthogonality only for single-connecting motion fields; however, for complex motion fields with many multi-connected and unconnected pixels, the reversible motion-compensated lifted Haar wavelet loses the property of orthogonality. A motion-compensated orthogonal transform that strictly maintains orthogonality for any motion field would be advantageous.